Energy and Enstrophy Study of the Time Relaxation Model

Abstract

This paper presents an investigation of the convergence of an Oseen type of problem for a fluid model known as Time Relaxation Model, TRM. Furthermore, conservation of energy and enstrophy of TRM are presented along with a dimensional analysis study of these properties. The paper contains two types of numerical experiments, one of which is based on finite element discretization that employs the Oseen type of problem for dealing with the nonlinearity of the TRM. The second type is the spectral related tests for the study of TRM dimensional analysis. Our numerical experiments confirm the theoretical findings.